On density estimation with superkernels

References

• Chancón , J. E. , Montanero , J. and Nogales , A. G. 2007 . A Note on Kernel Density Estimation at a Parametric Rate . Journal of Nonparametric Statistics , 19 ( 1 ) : 13 – 21 .
   Web of Science ®Google Scholar
• Davis , K. B. 1975 . Mean Square Error Properties of Density Estimates . Annals of Statistics , 3 ( 4 ) : 1025 – 1030 .
   Web of Science ®Google Scholar
• Davis , K. B. 1977 . Mean Integrated Square Error Properties of Density Estimates . Annals of Statistics , 5 ( 3 ) : 530 – 535 .
   Web of Science ®Google Scholar
• Devroye , L. 1992 . A Note on the Usefulness of Superkernels in Density Estimates . Annals of Statistics , 20 ( 4 ) : 2037 – 2056 .
   Web of Science ®Google Scholar
• Glad , I. K. , Hjort , N. L. and Ushakov , N. G. 2003 . Correction of Density Estimators that are Not Densities . Scandinavian Journal of Statistics , 30 ( 2 ) : 415 – 427 .
   Web of Science ®Google Scholar
• Gonzáles-Manteiga , W. , Sánches-Sellero , C. and Wand , P. M. 1996 . Accuracy of Binned Kernel Functional Approximations . Computational Statistics & Data Analysis , 22 ( 1 ) : 1 – 16 .
   Web of Science ®Google Scholar
• Hall , P. 1982 . The Influence of Rounding Errors on Some Nonparametric Estimators of a Density and its Derivatives . SIAM Journal on Applied Mathematics , 42 ( 2 ) : 390 – 399 .
   Web of Science ®Google Scholar
• Hall , P. and Wand , M. P. 1996 . On the Accuracy of Binned Kernel Density Estimators . Journal of Multivariate Analysis , 56 ( 2 ) : 165 – 184 .
   Web of Science ®Google Scholar
• Hansen , B. E. 2005 . Exact Mean Integrated Squared Error of Higher Order Kernel Estimators . Econometrics Theory , 21 ( 6 ) : 1031 – 1057 .
   Google Scholar
• Härdle , W. and Scott , D. W. 1992 . Smoothing by Weighted Averaging of Rounded Points . Computational Statistics , 7 ( 2 ) : 97 – 128 .
   Google Scholar
• Jones , M. C. 1989 . Discretized and Interpolated Kernel Density Estimates . Journal of the American Statistical Association , 84 ( 407 ) : 733 – 741 .
   Web of Science ®Google Scholar
• Jones , M. C. and Lotwick , H. W. 1983 . On the Errors Involved in Computing the Empirical Characteristic Function . Journal of Statistical Computation and Simulation , 17 ( 2 ) : 133 – 149 .
   Web of Science ®Google Scholar
• Marron , J. S. and Wand , M. P. 1992 . Exact Mean Integrated Squared Error . Annals of Statistics , 20 ( 2 ) : 712 – 736 .
   Web of Science ®Google Scholar
• Pawlak , M. and Stadtmüller , U. 1997 . Nonparametric Estimation of a Class of Smooth Functions . Journal of Nonparametric Statistics , 8 ( 2 ) : 149 – 183 .
   Google Scholar
• Politis , D. N. 2003 . Adaptive Bandwidth Choice . Journal of Nonparametric Statistics , 15 ( 4–5 ) : 517 – 533 .
   Web of Science ®Google Scholar
• Politis , D. N. and Romano , J. P. 1999 . Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order . Journal of Multivariate Analysis , 68 ( 1 ) : 1 – 25 .
   Web of Science ®Google Scholar
• Rafajlowicz , E. 1997 . Consistency of Orthogonal Series Density Estimators Based on Grouped Observations . IEEE Transactions on Information Theory , 43 ( 1 ) : 283 – 285 .
   Web of Science ®Google Scholar
• Reimer , L. 1998 . Scanning Electron Microscopy , 2 , Berlin, Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Scott , D. W. 1992 . Multivariate Density Estimation , New York : Wiley .
   Google Scholar
• Scott , D. W. and Sheather , S. J. 1985 . Kernel Density Estimation with Binned Data . Communications in Statistics – Theory and Methods , 14 ( 6 ) : 1353 – 1359 .
   Web of Science ®Google Scholar
• Ushakov , N. G. 2012 . A Note on Superkernel Density Estimators . Mathematical Methods of Statistics , 21 ( 1 ) : 61 – 68 .
   Google Scholar
• Ushakov , V. G. and Ushakov , N. G. 2000 . Some Inequalities for Characteristic Functions of Densities with Bounded Variation . Moscow University Computational Mathematics and Cybernetics , 19 ( 3 ) : 45 – 52 .
   Google Scholar
• Wand , M. P. 1994 . Fast Computation of Multivariate Kernel Estimators . Journal of Computational and Graphical Statistics , 3 ( 4 ) : 433 – 445 .
   Google Scholar
• Wand , M. P. and Jones , M. C. 1995 . Kernel Smoothing , London : Chapman and Hall .
   Google Scholar
• Watson , G. S. and Leadbetter , M. R. 1963 . On the Estimation of the Probability Density . Annals of Mathematical Statistics , 33 ( 2 ) : 480 – 491 .
   Google Scholar